Subgroups — #34020252

Order 18688.

1010 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989597	C₂	1	1	yes	maximal, characteristic
2	#22626494	C₂	1	2	yes	maximal
3	C₂×#17989550	C₂	1	1	yes	maximal, characteristic
4	#22625740	C₂	1	4	yes	maximal, complemented
5	#22625736	C₂	1	4	yes	maximal, complemented
6	#22625613	C₂	1	2	yes	maximal
7	C₂×#108×D₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×D₇₃⋊M₁₆	C₂²	1	1	yes	characteristic
9	C₂×#14556670	C₂²	1	2	yes	—
10	C₂×#14556670	C₂²	1	1	yes	characteristic
11	#17989597	C₄	1	2	yes	complemented
12	#17989597	C₄	1	2	yes	complemented
13	#17989597	C₂²	1	2	yes	—
14	#17989597	C₂²	1	2	yes	—
15	C₂×#14556660	C₄	1	2	yes	complemented
16	C₂×#14556659	C₄	1	2	yes	complemented
17	#17989553	C₂²	1	8	yes	—
18	#17989550	—	2	4	no	—
19	#17989550	C₄	1	2	yes	complemented
20	#17989550	C₄	1	2	yes	complemented
21	#17989550	C₄	1	2	yes	complemented
22	#17989550	C₄	1	2	yes	complemented
23	M₁₆×#64408	—	2	4	no	—
24	C₂×#14556645	C₂²	1	2	yes	—
25	C₂×C₈×#64408	C₂²	1	2	yes	—
26	#17989459	C₂²	1	8	yes	—
27	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
28	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
29	C₂×#14556527	C₄	1	1	yes	characteristic, complemented
30	C₂×#14556526	C₄	1	2	yes	complemented
31	#108×D₇₃	C₄	1	2	yes	complemented
32	#108×D₇₃	C₄	1	2	yes	complemented
33	#108×D₇₃	C₂²	1	2	yes	—
34	#108×D₇₃	C₂²	1	2	yes	—
35	C₂×#108×C₇₃	C₄	1	1	yes	characteristic, complemented
36	C₂×#11924038	Q₈	1	2	yes	—
37	D₇₃⋊M₁₆	C₂×C₄	1	2	yes	—
38	D₇₃⋊M₁₆	C₂×C₄	1	2	yes	—
39	D₇₃⋊M₁₆	D₄	1	2	yes	—
40	D₇₃⋊M₁₆	D₄	1	2	yes	—
41	C₂×#11924037	Q₈	1	2	yes	—
42	C₂×#11924036	C₂³	1	2	yes	—
43	#14556670	—	2	2	no	—
44	#14556670	—	2	2	no	—
45	#14556670	—	2	1	no	—
46	#14556670	—	2	1	no	—
47	#14556670	C₂×C₄	1	4	yes	—
48	#14556670	C₂×C₄	1	2	yes	—
49	#14556670	C₂×C₄	1	2	yes	—
50	#14556670	C₂³	1	4	yes	—
51	C₂×C₄⋊#64408	—	2	1	no	—
52	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
53	C₂×C₂²⋊#64408	—	2	1	no	—
54	C₂×C₂²⋊#64408	—	2	2	no	—
55	C₂×C₄×#64408	—	2	2	no	—
56	C₂×C₄×#64408	C₂³	1	2	yes	—
57	#14556660	C₂×C₄	1	4	yes	—
58	#14556660	C₂×C₄	1	4	yes	—
59	#14556659	C₂×C₄	1	4	yes	—
60	#14556659	C₂×C₄	1	4	yes	—
61	#14556645	—	2	8	no	—
62	#14556645	C₂×C₄	1	4	yes	complemented
63	#14556645	C₂×C₄	1	4	yes	complemented
64	C₈×#64408	—	2	8	no	—
65	C₈×#64408	C₂×C₄	1	4	yes	complemented
66	C₈×#64408	C₂×C₄	1	4	yes	complemented
67	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
68	C₂×#11924012	C₂×C₄	1	2	yes	—
69	C₂×#11924011	—	2	2	no	—
70	M₁₆×D₇₃	—	2	2	no	—
71	M₁₆×D₇₃	—	2	2	no	—
72	M₁₆×D₇₃	C₂×C₄	1	4	yes	—
73	M₁₆×D₇₃	C₂³	1	4	yes	—
74	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₇₃	—	2	2	no	—
76	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
87	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
88	#14556527	C₂×C₄	1	2	yes	complemented
89	#14556527	C₂×C₄	1	2	yes	complemented
90	#14556526	C₂×C₄	1	4	yes	complemented
91	#14556526	C₂×C₄	1	4	yes	complemented
92	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
93	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
94	#108×C₇₃	C₂×C₄	1	2	yes	complemented
95	#108×C₇₃	C₂×C₄	1	2	yes	complemented
96	C₂²×#64408	—	2	2	no	—
97	C₂²×#64408	—	2	4	no	—
98	#11924038	C₄⋊C₄	1	4	yes	—
99	#11924038	C₄⋊C₄	1	4	yes	—
100	#11924037	C₄⋊C₄	1	4	yes	—
101	#11924037	C₄⋊C₄	1	4	yes	—
102	#11924036	C₂²×C₄	1	4	yes	—
103	#11924036	C₂×D₄	1	4	yes	—
104	C₂×#10596833	C₂×Q₈	1	4	yes	—
105	C₄⋊#64408	—	2	2	no	—
106	C₄⋊#64408	—	2	2	no	—
107	C₄⋊#64408	—	2	4	no	—
108	C₄⋊#64408	C₂²×C₄	1	8	yes	—
109	C₂²⋊#64408	—	2	2	no	—
110	C₂²⋊#64408	—	2	2	no	—
111	C₂²⋊#64408	—	2	4	no	—
112	C₂²⋊#64408	—	2	4	no	—
113	C₄×#64408	—	2	4	no	—
114	C₄×#64408	—	2	4	no	—
115	C₄×#64408	—	2	2	no	—
116	C₄×#64408	C₂²×C₄	1	4	yes	—
117	C₂³×D₇₃	#41	1	1	yes	characteristic
118	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
127	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
128	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
129	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
130	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
131	#11924012	—	2	2	no	—
132	#11924012	C₂²×C₄	1	4	yes	—
133	#11924011	—	2	4	no	—
134	#11924011	—	2	4	no	—
135	C₂×#10596831	—	2	2	no	—
136	C₂×#10596831	C₄²	1	1	yes	characteristic
137	C₂×#10596831	C₄²	1	1	yes	characteristic
138	C₂×#10596831	C₄²	1	1	yes	characteristic
139	C₂×#10596831	C₄²	1	1	yes	characteristic
140	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
141	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
142	C₈×D₇₃	—	2	4	no	—
143	C₈×D₇₃	—	2	4	no	—
144	C₈×D₇₃	C₄²	1	1	yes	characteristic
145	C₈×D₇₃	C₄²	1	1	yes	characteristic
146	C₈×D₇₃	C₄²	1	1	yes	characteristic
147	C₈×D₇₃	C₄²	1	1	yes	characteristic
148	C₈×D₇₃	C₄²	1	1	yes	characteristic
149	C₈×D₇₃	C₄²	1	1	yes	characteristic
150	C₈×D₇₃	C₄²	1	1	yes	characteristic
151	C₈×D₇₃	C₄²	1	1	yes	characteristic
152	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
153	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
154	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
155	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
156	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
157	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
158	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
159	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
161	M₁₆×C₇₃	—	2	2	no	—
162	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
163	C₂×C₈×C₇₃	—	2	2	no	—
164	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
165	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
166	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
167	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
168	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
170	C₂³×C₇₃	C₄×Q₈	1	1	yes	characteristic
171	C₂²×D₇₃	—	4	2	no	—
172	C₂²×D₇₃	#117	1	1	yes	characteristic
173	C₂²×D₇₃	#117	1	1	yes	characteristic
174	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
175	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
176	C₂²×D₇₃	C₄×Q₈	1	1	yes	characteristic
177	C₂²×D₇₃	C₂×#41	1	1	yes	characteristic
178	C₂×#64408	—	2	4	no	—
179	C₂×#64408	—	2	8	no	—
180	C₂×#64408	—	4	4	no	—
181	C₂×#64408	—	8	4	no	—
182	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
184	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
188	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
191	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
192	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
193	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
194	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
195	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
196	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₄×D₇₃	#117	1	1	yes	characteristic
199	C₄×D₇₃	#117	1	1	yes	characteristic
200	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
201	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
202	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
203	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
204	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
205	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
206	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
207	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
208	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
209	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
210	#10596833	C₂×C₄⋊C₄	1	8	yes	—
211	C₈×C₇₃	—	2	4	no	—
212	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
213	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
214	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
215	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
216	#10596831	—	2	4	no	—
217	#10596831	C₂×C₄²	1	1	yes	characteristic
218	#10596831	C₂×C₄²	1	1	yes	characteristic
219	#10596831	C₂×C₄²	1	1	yes	characteristic
220	#10596831	C₂×C₄²	1	1	yes	characteristic
221	C₂²×C₇₃	—	4	1	no	—
222	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
223	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
224	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
225	C₂×D₇₃	—	2	2	no	—
226	C₂×D₇₃	—	2	2	no	—
227	C₂×D₇₃	—	2	2	no	—
228	C₂×D₇₃	—	4	1	no	—
229	C₂×D₇₃	—	4	1	no	—
230	C₂×D₇₃	—	4	1	no	—
231	C₂×D₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
232	C₂×D₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
233	C₂×D₇₃	C₂×#117	1	1	yes	characteristic
234	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
235	#64408	—	4	4	no	—
236	#64408	—	4	8	no	—
237	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
239	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
240	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
241	Dic₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
242	Dic₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
243	Dic₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
244	Dic₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
245	#20446	—	73	1	no	maximal, Sylow
246	C₂×C₇₃	—	2	1	no	—
247	C₂×C₇₃	—	2	1	no	—
248	C₂×C₇₃	—	2	1	no	—
249	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
250	D₇₃	—	2	1	no	—
251	D₇₃	—	2	1	no	—
252	D₇₃	—	2	1	no	—
253	D₇₃	#2957	1	2	yes	—
254	C₂²×#108	—	73	1	no	—
255	C₂×#427	—	73	1	no	—
256	#2873	—	73	2	no	—
257	C₂×#405	—	73	1	no	—
258	#1773	—	73	4	no	—
259	#1772	—	73	4	no	—
260	#1733	—	73	2	no	—
261	C₇₃	#20446	1	1	yes	characteristic, complemented, Sylow
262	C₂²×M₁₆	—	73	1	no	—
263	C₂²×M₁₆	—	73	2	no	—
264	C₂³×C₈	—	73	1	no	—
265	C₂×#117	—	73	1	no	—
266	C₂×#117	—	73	2	no	—
267	C₂×#108	—	73	2	no	—
268	C₂×#108	—	73	1	no	—
269	C₂×#108	—	73	2	no	—
270	C₂×#108	—	73	2	no	—
271	C₂×#108	—	73	2	no	—
272	C₂×#108	—	73	2	no	—
273	C₂×#108	#64408	1	1	yes	characteristic, complemented
274	#427	—	73	2	no	—
275	#427	—	73	2	no	—
276	#427	—	73	2	no	—
277	#427	—	73	2	no	—
278	C₂×#107	—	73	2	no	—
279	C₂×#106	—	73	2	no	—
280	#405	—	73	2	no	—
281	#405	—	73	2	no	—
282	#405	—	73	2	no	—
283	#405	—	73	2	no	—
284	#405	—	73	8	no	—
285	#405	—	146	4	no	—
286	C₄×M₁₆	—	146	4	no	—
287	C₂×#97	—	73	2	no	—
288	C₂×C₄×C₈	—	73	2	no	—
289	#339	—	73	8	no	—
290	C₂³×C₄	—	73	1	no	—
291	C₂×M₁₆	—	73	2	no	—
292	C₂×M₁₆	—	73	2	no	—
293	C₂×M₁₆	—	73	2	no	—
294	C₂×M₁₆	—	73	2	no	—
295	C₂×M₁₆	—	73	2	no	—
296	C₂×M₁₆	—	73	2	no	—
297	C₂×M₁₆	—	73	2	no	—
298	C₂×M₁₆	—	73	4	no	—
299	C₂×M₁₆	—	73	4	no	—
300	C₂×M₁₆	—	146	2	no	—
301	C₂×M₁₆	—	146	2	no	—
302	C₂×M₁₆	—	146	2	no	—
303	C₂×M₁₆	C₂×#64408	1	2	yes	—
304	C₂²×C₈	—	73	2	no	—
305	C₂²×C₈	—	73	1	no	—
306	C₂²×C₈	—	73	1	no	—
307	C₂²×C₈	—	73	1	no	—
308	C₂²×C₈	—	73	1	no	—
309	C₂²×C₈	—	73	1	no	—
310	C₂²×C₈	—	73	1	no	—
311	C₂²×C₈	—	73	1	no	—
312	C₂²×C₈	—	73	1	no	—
313	C₂²×C₈	—	73	1	no	—
314	C₂²×C₈	—	73	1	no	—
315	C₂²×C₈	—	73	1	no	—
316	C₂²×C₈	—	73	1	no	—
317	C₂²×C₈	—	73	1	no	—
318	C₂²×C₈	—	146	2	no	—
319	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
320	#117	—	73	2	no	—
321	#117	—	73	2	no	—
322	#117	—	73	4	no	—
323	#117	—	73	4	no	—
324	#117	—	146	2	no	—
325	#117	—	146	1	no	—
326	#117	—	146	1	no	—
327	#117	—	146	2	no	—
328	C₂×C₄⋊C₄	—	73	4	no	—
329	C₂×C₄⋊C₄	—	146	1	no	—
330	C₂×C₂²⋊C₄	—	146	1	no	—
331	C₂×C₂²⋊C₄	—	146	2	no	—
332	C₂×C₄²	—	73	2	no	—
333	C₂×C₄²	—	146	2	no	—
334	#108	—	73	4	no	—
335	#108	—	73	4	no	—
336	#108	—	73	2	no	—
337	#108	—	73	2	no	—
338	#108	C₂×#64408	1	2	yes	complemented
339	#108	C₂×#64408	1	2	yes	complemented
340	#107	—	73	4	no	—
341	#107	—	73	4	no	—
342	#106	—	73	4	no	—
343	#106	—	73	4	no	—
344	#97	—	73	4	no	—
345	#97	—	73	4	no	—
346	#97	—	146	8	no	—
347	C₄×C₈	—	73	4	no	—
348	C₄×C₈	—	73	4	no	—
349	C₄×C₈	—	146	8	no	—
350	C₂⁴	—	73	1	no	—
351	C₂²×C₄	—	73	1	no	—
352	C₂²×C₄	—	73	1	no	—
353	C₂²×C₄	—	73	1	no	—
354	C₂²×C₄	—	73	1	no	—
355	C₂²×C₄	—	73	1	no	—
356	C₂²×C₄	—	73	1	no	—
357	C₂²×C₄	—	73	1	no	—
358	C₂²×C₄	—	73	1	no	—
359	C₂²×C₄	—	73	1	no	—
360	C₂²×C₄	—	73	1	no	—
361	C₂²×C₄	—	73	1	no	—
362	C₂²×C₄	—	73	1	no	—
363	C₂²×C₄	—	73	1	no	—
364	C₂²×C₄	—	146	2	no	—
365	C₂²×C₄	—	146	4	no	—
366	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
367	M₁₆	—	2	2	no	—
368	M₁₆	—	73	4	no	—
369	M₁₆	—	73	4	no	—
370	M₁₆	—	73	4	no	—
371	M₁₆	—	73	4	no	—
372	M₁₆	—	73	4	no	—
373	M₁₆	—	146	4	no	—
374	M₁₆	—	146	4	no	—
375	M₁₆	—	146	2	no	—
376	M₁₆	C₂²×#64408	1	4	yes	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	73	4	no	—
379	C₂×C₈	—	73	4	no	—
380	C₂×C₈	—	73	4	no	—
381	C₂×C₈	—	73	1	no	—
382	C₂×C₈	—	73	1	no	—
383	C₂×C₈	—	73	1	no	—
384	C₂×C₈	—	73	1	no	—
385	C₂×C₈	—	73	1	no	—
386	C₂×C₈	—	73	1	no	—
387	C₂×C₈	—	73	1	no	—
388	C₂×C₈	—	73	1	no	—
389	C₂×C₈	—	73	1	no	—
390	C₂×C₈	—	73	1	no	—
391	C₂×C₈	—	73	1	no	—
392	C₂×C₈	—	73	1	no	—
393	C₂×C₈	—	73	1	no	—
394	C₂×C₈	—	73	1	no	—
395	C₂×C₈	—	73	1	no	—
396	C₂×C₈	—	73	1	no	—
397	C₂×C₈	—	73	1	no	—
398	C₂×C₈	—	73	1	no	—
399	C₂×C₈	—	73	1	no	—
400	C₂×C₈	—	73	1	no	—
401	C₂×C₈	—	73	1	no	—
402	C₂×C₈	—	73	1	no	—
403	C₂×C₈	—	146	4	no	—
404	C₂×C₈	—	146	4	no	—
405	C₂×C₈	—	146	2	no	—
406	C₂×C₈	C₄×#64408	1	1	yes	characteristic
407	C₂×C₈	C₄×#64408	1	1	yes	characteristic
408	C₂×C₈	C₄×#64408	1	1	yes	characteristic
409	C₂×C₈	C₄×#64408	1	1	yes	characteristic
410	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
411	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
412	C₄⋊C₄	—	73	8	no	—
413	C₄⋊C₄	—	146	4	no	—
414	C₄⋊C₄	—	146	2	no	—
415	C₄⋊C₄	—	146	2	no	—
416	C₂²⋊C₄	—	146	2	no	—
417	C₂²⋊C₄	—	146	2	no	—
418	C₂²⋊C₄	—	146	4	no	—
419	C₂²⋊C₄	—	146	4	no	—
420	C₄²	—	73	4	no	—
421	C₄²	—	146	4	no	—
422	C₄²	—	146	2	no	—
423	C₄²	—	146	4	no	—
424	C₂³	—	292	2	no	—
425	C₂³	—	73	1	no	—
426	C₂³	—	73	1	no	—
427	C₂³	—	73	1	no	—
428	C₂³	—	73	1	no	—
429	C₂³	—	73	1	no	—
430	C₂³	—	73	1	no	—
431	C₂³	Q₈×#64408	1	1	yes	characteristic
432	C₂×C₄	—	292	4	no	—
433	C₂×C₄	—	584	4	no	—
434	C₂×C₄	—	73	1	no	—
435	C₂×C₄	—	73	1	no	—
436	C₂×C₄	—	73	1	no	—
437	C₂×C₄	—	73	1	no	—
438	C₂×C₄	—	73	1	no	—
439	C₂×C₄	—	73	1	no	—
440	C₂×C₄	—	73	1	no	—
441	C₂×C₄	—	73	1	no	—
442	C₂×C₄	—	73	1	no	—
443	C₂×C₄	—	73	1	no	—
444	C₂×C₄	—	73	1	no	—
445	C₂×C₄	—	73	1	no	—
446	C₂×C₄	—	73	1	no	—
447	C₂×C₄	—	73	1	no	—
448	C₂×C₄	—	73	1	no	—
449	C₂×C₄	—	73	1	no	—
450	C₂×C₄	—	73	1	no	—
451	C₂×C₄	—	73	1	no	—
452	C₂×C₄	—	73	1	no	—
453	C₂×C₄	—	73	1	no	—
454	C₂×C₄	—	73	1	no	—
455	C₂×C₄	—	73	1	no	—
456	C₂×C₄	—	146	4	no	—
457	C₂×C₄	—	146	8	no	—
458	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
459	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
460	C₂×C₄	D₄×#64408	1	1	yes	characteristic
461	C₂×C₄	D₄×#64408	1	1	yes	characteristic
462	C₂×C₄	Q₈×#64408	1	1	yes	characteristic
463	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
464	C₈	—	2	4	no	—
465	C₈	—	73	8	no	—
466	C₈	—	73	1	no	—
467	C₈	—	73	1	no	—
468	C₈	—	73	1	no	—
469	C₈	—	73	1	no	—
470	C₈	—	146	4	no	—
471	C₈	C₂×C₄×#64408	1	1	yes	characteristic
472	C₈	C₂×C₄×#64408	1	1	yes	characteristic
473	C₈	C₂×C₄×#64408	1	1	yes	characteristic
474	C₈	C₂×C₄×#64408	1	1	yes	characteristic
475	C₂²	—	4	1	no	—
476	C₂²	—	292	1	no	—
477	C₂²	—	292	1	no	—
478	C₂²	—	292	1	no	—
479	C₂²	—	73	1	no	—
480	C₂²	—	73	1	no	—
481	C₂²	—	73	1	no	—
482	C₂²	—	73	1	no	—
483	C₂²	—	146	2	no	—
484	C₂²	—	146	2	no	—
485	C₂²	—	146	2	no	—
486	C₂²	C₄⋊C₄×#64408	1	1	yes	characteristic
487	C₂²	C₄⋊C₄×#64408	1	1	yes	characteristic
488	C₂²	C₂×Q₈×#64408	1	1	yes	characteristic
489	C₄	—	292	8	no	—
490	C₄	—	292	4	no	—
491	C₄	—	73	1	no	—
492	C₄	—	73	1	no	—
493	C₄	—	73	1	no	—
494	C₄	—	73	1	no	—
495	C₄	C₄⋊C₄×#64408	1	1	yes	characteristic
496	C₄	C₄⋊C₄×#64408	1	1	yes	characteristic
497	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
498	C₄	C₂×D₄×#64408	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	2	1	no	—
502	C₂	—	73	2	no	—
503	C₂	—	146	1	no	—
504	C₂	—	146	1	no	—
505	C₂	—	146	1	no	—
506	C₂	C₂×C₄⋊C₄×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×#64408
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₂×#108×C₇₃	C₄
socle	C₂×C₇₃	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₇₃	#41
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₂×#108	#64408
hypocenter	C₇₃	#20446
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #22625740	C₂	semidirect
5. #22625736	C₂	semidirect
11. #17989597	C₄	semidirect
12. #17989597	C₄	semidirect
15. C₂×#14556660	C₄	semidirect
16. C₂×#14556659	C₄	semidirect
19. #17989550	C₄	semidirect
20. #17989550	C₄	semidirect
21. #17989550	C₄	semidirect
22. #17989550	C₄	semidirect
29. C₂×#14556527	C₄	semidirect
30. C₂×#14556526	C₄	semidirect
31. #108×D₇₃	C₄	semidirect
32. #108×D₇₃	C₄	semidirect
35. C₂×#108×C₇₃	C₄	semidirect
62. #14556645	C₂×C₄	semidirect
63. #14556645	C₂×C₄	semidirect
65. C₈×#64408	C₂×C₄	semidirect
66. C₈×#64408	C₂×C₄	semidirect
88. #14556527	C₂×C₄	semidirect
89. #14556527	C₂×C₄	semidirect
90. #14556526	C₂×C₄	semidirect
91. #14556526	C₂×C₄	semidirect
94. #108×C₇₃	C₂×C₄	semidirect
95. #108×C₇₃	C₂×C₄	semidirect
261. C₇₃	#20446	semidirect
273. C₂×#108	#64408	semidirect
338. #108	C₂×#64408	semidirect
339. #108	C₂×#64408	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#17989597	2
#22626494	2
C₂×#17989550	2
#22625740	2
#22625736	2
#22625613	2
C₂×#108×D₇₃	2
#20446	73